process of combining 2 meshes into one not in object mode but in edit mode?
What are you trying to do? Deleting the cone, adding it in object mode, and then using ctrl + j just gets you back to where you started. Its the same as adding it in edit mode.

Assuming you want to join them to one flowing mesh.


Select the edge loops with alt + rightclick
Search in the space search menu for bridge edge loops
Select it from the search


Before:


After: